Question

use the quadratic formula to solve for x.
9x^2 + 5x - 1 = 0
(if there is more than one solution, separate them with commas.)
x =

Explanation:

Step1: Identify coefficients

For the quadratic equation $ax^{2}+bx + c = 0$, here $a = 9$, $b = 5$, $c=-1$.

Step2: Write the quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$.

Step3: Substitute coefficients

Substitute $a = 9$, $b = 5$, $c=-1$ into the formula:
\[

$$\begin{align*} x&=\frac{-5\pm\sqrt{5^{2}-4\times9\times(-1)}}{2\times9}\\ &=\frac{-5\pm\sqrt{25 + 36}}{18}\\ &=\frac{-5\pm\sqrt{61}}{18} \end{align*}$$

\]

Answer:

$x=\frac{-5+\sqrt{61}}{18},\frac{-5 - \sqrt{61}}{18}$